Over at Open Borders: The Case, Vipul Naik was discussing the concept of “genotypic IQ.” He notes:
My main beef is that I find the concept of “genetic IQ” ill defined and poorly conceived. Yes, there is a heritable component to variation in IQ, and yes, it’s possible that differences in gene frequencies between races is responsible for differences in observed IQs. In fact, I’d be very surprised if none of the genes that affect IQ were found to vary in frequency between human subpopulations…
But, talk of genetic IQ presupposes a kind of “holding environment constant” or some kind of maximal, optimal environment in which everybody can fulfill their genetic potential. Most IQ “hard hereditarians” hold this sort of view. I think this is plausible, but I have doubts. It’s possible that talk of “genetic IQ” is like talk of “genetic income” — certainly, genes affect income and part of the variation in income is heritable, but the concept of “genetic income” doesn’t make sense. On the other hand, it may be possible that IQ is more like “number of hands” in that there is a genetic predisposition to a certain value, barring specific environmental catastrophes….
…Still, one can define “US middle-class genetic IQ”: what would a person’s IQ be if he/she were raised in a middle-class US household today?
Vipul Naik is right that the concept of “genotypic IQ” is ill defined. It’s tempting to operationalize it as Vipul does but such attempts are doomed to confusion because heritability is a population, age, and test specific estimate. There is no set “US middle class heritability” so there can be no set “US middle class genetic IQ,” so defined. It would be much clearer to talk, instead, about genetic effects, where we understood this to refer to the magnitude of IQ influencing effects exerted by the genome. This could then be contrasted with environmental effects and placed in context to population, age, and test specific heritability coefficients. To help readers out, I created the following simplified chart which shows the relation between within group heritability, genetic effect, and the magnitude of a between group phenotypic difference, assuming no environmental effect (and, of course, measure invariance):
Since environmentality is 1-h^2 one can use the same chart to see the relation between within group envrionmentality, environmental effect, and the magnitude of a between group phenotypic difference, assuming no genetic effect. And since environmental and genetic effects, under the simplest model, are additive one can see the relation between various combinations of the two effects.
(To take a plausible scenario: African Americans differ in genetic effects from European Americans by 1 SD. As such, by adulthood, when the heritability of IQ is typically 0.7, the phenotypic gap conditioned on genes is d = 0.85. The two subpopulations also differ in shared environments by 0.5 SD. Since the shared environmentality of IQ is about 0.15 by adulthood (or half of the total environmentality), this results in a phenotypic gap of d = 0.2 conditioned on the environment. The total resultant difference is about 1.05 SD.)
We can still talk about “genotypic IQ,” of course. Using Vipul’s operalization, “genotypic IQ” is, simply:
genetic effect x squared heritability
This just isn’t our starting place.